Interacting partially directed self avoiding walk : scaling limits

This paper is dedicated to the investigation of a $1+1$ dimensional self-interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW and introduced in \cite{ZL68} by Zwanzig and Lauritzen to study the collapse transition of an homopolymer dipped in a poor solvant. In \cite{POBG93}, physicists displayed numerical results concerning the typical growth rate of some geometric features of the path as its length $L$ diverges. From this perspective the quantities of interest are the projections of the path onto the horizontal axis (also called horizontal extension) and onto the vertical axis for which it is useful to define the lower and the upper envelopes of the path. With the help of a new random walk representation, we proved in \cite{CNGP13} that the path grows horizontally like $\sqrt{L}$ in its collapsed regime and that, once rescaled by $\sqrt{L}$ vertically and horizontally, its upper and lower envelopes converge to some deterministic Wulff shapes. In the present paper, we bring the geometric investigation of the path several steps further. In the extended regime, we prove a law of large number for the horizontal extension of the polymer rescaled by its total length $L$, we provide a precise asymptotics of the partition function and we show that its lower and upper envelopes, once rescaled in time by $L$ and in space by $\sqrt{L}$, converge to the same Brownian motion. At criticality, we identify the limiting distribution of the horizontal extension rescaled by $L^{2/3}$ and we show that the excess partition function decays as $L^{2/3}$ with an explicit prefactor. In the collapsed regime, we identify the joint limiting distribution of the fluctuations of the upper and lower envelopes around their associated limiting Wulff shapes, rescaled in time by $\sqrt{L}$ and in space by $L^{1/4}$.Comment: 52 pages, 4 figure

The discrete-time parabolic Anderson model with heavy-tailed potential

We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed (1+d)-dimensional polymer interacting with a random potential, which is constant in the deterministic direction and i.i.d. in the d orthogonal directions. The potential at each site is a positive random variable with a polynomial tail at infinity. We show that, as the size of the system diverges, the polymer extremity is localized almost surely at one single point which grows ballistically. We give an explicit characterization of the localization point and of the typical paths of the model.Comment: 32 page

Laser and carbon : nanotube synthesis and annealing

Thanks to their predicted and measured properties, carbon nanotubes (CNTs) are becoming viable and superior alternatives to many of materials science’s established materials. Yet, although the divide between model and reality has narrowed, insufficient CNT quality and purity remain major hindrances to the performance of most CNT-based materials. Furthermore, CNT precursors are overwhelmingly high-purity petrochemical substances, hampering sustainable and widespread adoption of CNTs. These two identified challenges were addressed towards synthesis energy and cost efficiency, sustainability and material performance. To this end, single-wall CNTs (SWCNTs) were synthesised in a custom-built oven laser apparatus as the object of this study. Laser annealing was found to quickly and drastically recrystallise defects and remove impurities as measured by Raman spectroscopy, thermogravimetry, electrical resistance and hydrogen adsorption measurements. Results could be reproduced at the micro- and millimetre scale. Composite processing related damage, artificially introduced into SWCNTs, was almost completely reversed by laser annealing. Quality and purity levels equal to that of commercial tubes could be achieved through this technique. A waste product of petroleum refining, fluid catalytic cracking catalyst residue, was successfully employed as carbon precursor for SWCNT synthesis, as well as silica nanowires, onion-like carbons and carbon nanodiamonds.Aufgrund Ihrer vielfach prognostizierten aber auch bekannten Eigenschaften, werden Kohlenstoff-Nanoröhrchen (CNTs) zu konkurrenzfähigen und teilweise überlegenen Alternativen zu vielen in der Materialforschung etablierten Materialien. Obwohl sich die „Kluft“ zwischen Modellvorstellungen und Realität verkleinert hat, sind die unzureichende CNT-Qualität und Reinheit noch immer wesentliche Hindernisse für die Performance der meisten CNT-basierten Materialien. Darüber hinaus sind CNT-Vorgänger überwiegend hochreine petrochemische Substanzen, die eine Akzeptanz von CNTs erschweren. Diese Arbeit befasst sich mit den damit verknüpften Herausforderungen nämlich den Zielen Energie-/Kosteneffizienz, Nachhaltigkeit und Performance. Zu diesem Zweck wurden einwandige CNTs (SWCNTs) in einem speziellen Ofen, der mit einem Hochleistungslaser kombiniert wurde, synthetisiert und näher studiert. Die Laserbehandlung heilt Defekte und entfernt Verunreinigungen schnell und effizient. Dies wurde durch Raman-Spektroskopie, Thermogravimetrie, elektrische Widerstandsmessung und schließlich Wasserstoff-Adsorption bestätigt. Die Ergebnisse konnten im Mikro- und Millimeterbereich reproduziert werden. Herstellungsbedingte Defekte in den SWCNTs konnten durch Laserglühen fast vollständig beseitigt werden. Durch diese Technik konnten Qualität und Reinheitsgrade erreicht werden, die denen von handelsüblichen Nanoröhrchen entsprechen. Katalysatorrückstände des Cracking Prozesses während der Erdölraffination wurden dabei für die Synthese von SWCNTs, sowie Silica-Nanodrähten, „Onion-like Carbon“ und Kohlenstoff- Nanodiamanten eingesetzt

Passive tomography for elastic waves in solids

In this paper we derive relations between the cross-correlation of ambient noises recorded at two different points and the Green's function of the elastic waves in a medium with viscous damping. The Green's function allows to estimate physical parameters such as speeds or distances. Furthermore, this work is extended by introducing the Green's correlation function proposed by J-L. Lacoume in [Lacoume07]. Some recent works proved the possible reconstruction of the Green's function for scalar waves from the cross-correlation function of ambient noise. In this work, we consider vector waves propagating in a three dimensional solid medium. Two approaches are developed. Firstly, we extend theoretical derivations proposed by Y. Colin de Verdi`ere in [ColinDeVerdiere09], relating cross-correlation of scalar waves to 1D Green's function using linear operator theory. The second approach recasts the three dimensional problem in the framework of Fourier theory. This allows to improve physical understanding of the underlying physical processes as outlined in [Lacoume07].Comment: 24 page

Convolutional neural network-based onboard band selection for hyperspectral data with coarse band-to-band alignment

Band selection is a key strategy to address the challenges of managing large hyperspectral datasets and reduce the dimensionality problem associated with the simultaneous analysis of hundreds of spectral bands. However, the computational complexity of traditional methods makes the algorithms difficult to be deployed on board satellites. This is especially true for Small Satellites with limited computational and power resources. Moreover, existing band selection techniques often require the hypercube to be processed at least at Level-1B product, i.e., the bands need to be finely aligned before selecting them, demanding more computational resources for the on-board computer. This study presents a novel neural network-based approach for on-board band selection using data with coarse band-to-band aligned. This methodology not only simplifies the pre-processing requirements, but also opens new possibilities for efficient hyperspectral imaging from space on-board Small Satellites, such as classification, change and target detection.This project was part of the project "GENESIS: GNSS Environmental and Societal Missions – Subproject UPC", Grant PID2021-126436OB-C21 funded by the Ministerio de Ciencia e Investigación (MCIN)/Agencia Estatal de Investigación (AEI)/10.13039/501100011033 and EU FEDER “Una manera de hacer Europa”, and by a FPU fellowship from the Spanish Ministry of Education. Part of this work has also been possible thanks to the Italian Space Agency (ASI) that granted access to its PRISMA database (http://prisma.asi.it/).Peer ReviewedPostprint (published version